I've just tried to find out the specifications for the Ultimate Ears Boom 2, but without much luck. The page that claims to have a manual for that model is blocked as a malicious site and the Ultimate Ears site is less than helpful.
From what I can see, the Boom 2 model does not have a cable connection option (an AUX input socket). As a indication of how this can catch people out, I have just checked my JBL Charge 3. Below is a view of the connections on my model of JBL Charge 3:

But here's my point: JBL updated the Charge 3 to add new features, but as far as I can tell they dropped the AUX input. So one could buy a Charge 3 thinking it would have an AUX input, but discover they'd bought the newer model that does not have AUX. (You've already had one shop give you incorrect information, so there's every possibility that the same thing may happen again.) I will have to leave you to decide whether or not my points are valid. I say they are...
At this point, I think you need to confirm (to yourself) that you do have an iPod Classic, as many people refer to almost any model of iPod as a Classic. No point in all of this discussion if you actually have an iPod Touch that does have Bluetooth. If your iPod looks like the one shown below:

... then it is an iPod Classic; it has no Bluetooth and your options to connect it to speakers (or amplifiers) are as follows:
- use a 3.5mm to 3.5mm cable from the iPod's headphone socket to the AUX input socket on the speaker (if it has one). It should be easy enough to buy a 3.5mm to 3.5mm cable, which you would need
- use an iPod's 30-pin dock cable to go into a dock stand that has a 3.5mm outlet. (I doubt that you will find one, even second hand). It's also more clutter
- buy a Bluetooth transmitter, designed for the iPod's 30-pin dock connector, to give your Classic a Bluetooth output. However - these devices are now hard to find and you would need to make sure it is one designed for the 30-pin connector (as they are types that do not work like that) - AND you need to understand that these transmitters take their power from the iPod, which will cause the iPod's battery to run down very quickly
Of the three types I've mentioned, only the first one is actually practical today.
There's another thing to consider:
the iPod Classic uses a hard drive (a turning disc), and these discs fail. You might go through all the necessary work to buy what you need (as I have suggested) only for the iPod's hard drive to fail a day later, or even for the battery to give up.
Might I suggest an alternative?
If you have a smartphone (either an iPhone or an Android), perhaps it's time to consider using that as your music source as it will have Bluetooth, allowing you to use a Bluetooth speaker. I assume from what you have told us that you have music that you've bought (either on CD, or possibly as digital purchases from the iTunes Store). Even if you have an Android phone, all of those purchases can be used on it, although not with iTunes. Instead, you can use a well-known alternative (Media Monkey) to manage the music on the phone.
I can almost guarantee that at some stage, someone will suggest that you should use Apple Music, Amazon Music or Spotify (etc.), all of which are monthly subscription services. If you already own music, you don't need to pay for a monthly service, just to listen to the same music that you already own.